If $y<0$, find the range of all possible values of $y$ such that $\lceil{y}\rceil\cdot\lfloor{y}\rfloor=110$.  Express your answer using interval notation.
Solution: As long as $y$ is not an integer, we can define $\lceil{y}\rceil$ as $x$ and $\lfloor{y}\rfloor$ as $x-1$. If we plug these expressions into the given equation, we get  \begin{align*} x(x-1)&=110
\\\Rightarrow\qquad x^2-x&=110
\\\Rightarrow\qquad x^2-x-110&=0
\\\Rightarrow\qquad (x-11)(x+10)&=0
\end{align*}This yields $x=11$ and $x=-10$ as two possible values of $x$. However since the problem states that $y<0$ and $x=\lceil{y}\rceil$, $x$ cannot be a positive integer. This allows us to eliminate $11$, leaving the $-10$ as the only possible value of $x$. Since $x=\lceil{y}\rceil=-10$, and $x-1=\lfloor{y}\rfloor=-11$, $y$ must be between the integers $-10$ and $-11$. Therefore, our final answer is $-11<y<-10,$ or $y \in \boxed{(-11, -10)}$ in interval notation.